This is the first request I've seen in my (admittedly short) time here where I wouldn't recommend an Arduino !!!
I'm not much aware of the more advanced stuff out there, but my only thought for advice is regarding modularity:
It seems to me that modular design is sort of built-in to all dev boards in a way, being connected to peripherals via pin headers. Simplifying the hardware connections with ribbon cables can make it easier to connect & disconnect. This keeps the system flexible.
With a $500 budget, I am guessing that going deeper into modular design will get you above that price range in a hurry. I guess what I am getting at is it seems to me that adding "blocks" of new hardware will be fairly common for any MCU you pick, and you can make it easier to connect these blocks of hardware by applying just the simplest of cleverness to connection method, ie. the ribbon cable and pin header strip mentioned earlier or maybe some other ideas which you may see in others' projects along the way.
My other thought is that it seems like most chip UIs routinely deal with at least two and often more languages, C being the most common, so you're probably in good shape there as far as being able to choose from several. Getting into scripts is another thing I know almost nothing about and that may get you into another whole different thing, but waltr referred to things with Linux installed which may likely be your fit. From what I've seen, seems like it's not uncommon for more powerful processors to have some form of Linux for an OS, whether pre-installed or not, and that would obviously send you very quickly into some very versatile programming possibilities. I will defer specific recommendations to the knowledgeable, which I am most definitely not.
The only other piece of advice I can offer is what I usually say to anyone just starting to delve in:
If you get too complex an idea to start with, it is common to get above your raisin and quit on it before you get in very far. $500 that ends up going nowhere is much more expensive than $500 that goes where you wanted it to go. Depending on your skill set, it may behoove you to start with something simple just to get some success under your belt before moving to the grand idea. You obviously have plenty of programming chops to handle the tough stuff, but getting that to work with the robot motors and other peripherals can take a while depending on what you choose for all that.
With this in mind, it may be worth considering a much simpler robot to begin with, which can be MUCH less expensive to start with, and will still be something you can expand on later. What I'm thinking is that you can develop your rolling chassis and some peripherals (the mechanical stuff), which you need to do on any robot unless it's a "plug & play" kit. Once you have that working OK, it should be a very simple matter to remove the basic MCU and replace it with a more powerful and capable one so you can expand what it can do, i.e. video processing, etc. In this case, I still would still suggest something other than Arduino since it only
kind of uses C (at least with it's IDE). Basically you'd just need a programmer for the chip and whatever connection it needs (ISP in the case of Atmel chips).
The Axon, available through this site, seems to be a pretty powerful and well-designed MCU and is probably be worth consideration. I think it
does not require an external programmer too, so $30 saved there.
Good luck.